Niching Evolution Strategies for Simultaneously Finding Global and Pareto Optimal Solutions

Abstract

Many real world optimization problems turn out to be multi-objective optimization problems revealing a remarkable number of locally optimal solutions corresponding to the chosen objective function. Therefore, it seems desirable to detect as many of those solutions with as few objective function calls as possible. A Niching Higher Order Evolution Strategy (NES) can successfully be applied to locate a large number of these local solutions during a single optimization run. Additionally, it turns out that all of these solutions can be found next to the front of non-dominated solutions. Therefore, evaluating more than one objective function (in parallel or in series) yields a good approximation of the Pareto-optimal front. The proposed method will be tested against several test functions and then applied to the solution of a magnetic shunting problem.